Pour some clear liquid hand soap into a short, wide tumbler so that it is about one quarter full.

Note: alternatively, you can also use glucose syrup, pure glycerine or clear shampoo.

Fill a taller, narrower glass with water. The water will prevent this glass being buoyant when submerged in the wider glass filled with liquid soap and allow it to sink instead.

Put the narrow glass inside the wider glass so that it sinks into the liquid soap. The soap level should rise about half way up the sides of the shorter tumbler (top it up with more liquid soap if necessary).

Clamp three large fold-back paperclips* around the rim of the short, wide glass leaving space for a fourth to be added after the following step.

* 32 or 41 millimetre fold-back clips should do the trick, but it depends on the difference in the diameters of your two glasses.

Squirt a little liquid soap into three separate cups and add one or two drops of food dye to each (you don't need much.) Stir thoroughly to mix the food dye into the liquid soap, but wait for any bubbles you mixed in to rise to the surface.

When the coloured soap and the clear soap in the wide glass are all free of air bubbles, use an eyedropper or a drinking straw to pipette a blob of each of the three colours into the clear soap.

Now add the fourth fold-back paperclip to the rim of the wide glass.

The handles on the fold back clips press against the inner narrow glass, which helps to keep it concentric with the wider outer glass while you rotate it during the next step.

Press down on the paper clips to hold the short outer tumbler still while you carefully and slowly rotate the inner glass, keeping the two as concentric as possible. The coloured blobs will become a smear.

Now slowly and carefully rotate the inner glass back in the opposite direction by the same number of turns and the smear will magically turn back into three separate blobs.

What's going on?

The amazing "unmixing demonstration", as it is known, was first published in the April 1960 edition of the American Journal of Physics by an oil industry scientist called John P Heller. University lecturers have been wowing fluid mechanics students with it ever since.

Heller used glycerine (also known as glycerin or glycerol) instead of soap and a fancy apparatus called a 'Couette viscometer' instead of cheap household glassware. A Couette viscometer is basically one cylinder inside another with a liquid to be analysed in between. Here's an impressive version of the demonstration with a perfectly engineered apparatus.

The resistance to rotation of the inner cylinder is proportional to the liquid's viscosity, hence the name 'viscometer'. Viscosity, you are probably aware, is an important property of lubricants such as engine oils.

But what you're probably really wondering is how and why this "unmixing" business is possible because it so brazenly defies our everyday experience of liquids. The strange phenomenon you are witnessing is called 'laminar flow'. It is the opposite of 'turbulent flow', which you are probably much more familiar with. You can see both these kinds of flow when you extinguish a burning candle in a very still room. The stream of hot rising smoke starts off smooth and straight. That's laminar flow. But then, at some height above the wick, the smooth smoke stream suddenly breaks up into a wobble and may even turn back on itself. That's turbulent flow. It is chaotic and, therefore, impossible to predict.

Actually, turbulent flow may not be completely impossible to predict but right now, nobody knows. A solution to this problem is potentially so valuable though that the Clay Mathematics Institute has offered a one million dollar reward for anyone who "makes substantial progress toward a mathematical theory" that describes it. I am not kidding. The institute has already awarded one such prize to Dr Grigoriy Perelman for the resolution of another problem called the Poincaré conjecture (he amazingly declined the offer) and they offer the same bounty for five other brain-shattering mathematical problems, collectively known as the Millennium Prize Problems.

The difficulty in predicting non-laminar fluid flow is that, while forecasting a single molecule's motion might sound easy, there are billions upon trillions of molecules in a cup of any given liquid. The laws governing each molecule's motion are simple enough but with so many of them pushing and pulling each other in every conceivable direction, the problem of tracking any single one is astronomically huge.

To successfully tame this chaotic branch of fluid dynamics, someone will need to successfully solve the Navier-Stokes equations. So far, nobody has (hence the prize.) If you fancy yourself as a mathematical whiz, here's a detailed description of the problem.

This is not some esoteric problem only bored physicists care about, by the way. Designing new aeroplanes, for instance, would be much quicker and cheaper if engineers could more accurately predict the way air will flow over the wings and fuselage. Instead, they currently have to build expensive models and test them in expensive wind tunnels, which is slow and, well, expensive. The secret to reduced drag and therefore better fuel economy and cheaper air travel could also be lurking in the solution to the Navier-Stokes equations. This Catalyst story reveals the magnitude and expense of the problem.

So, back to the amazing reappearing blobs of coloured liquid soap. There are two main reasons the "unmixing demonstration" works. First, the flow is laminar. To be laminar, the liquid must be dense and viscous enough, and the motion should not be too fast. Second, thanks to the relatively simple and precise geometry of two concentric cylinders, the motion is almost perfectly reversible.

If you look down into the space between the outer and inner glass after the rotation, however, you will notice that the blobs are not really "mixing" together. Each one is actually dragged out to form a spiral. If you wait too long, a process called diffusion might ruin your demonstration by causing two adjacent spiral arms to combine, which will destroy the result.

The other big problem with the simple apparatus in this DIY home version of the demonstration is that the axis of the inner glass is not perfectly fixed and therefore tends to wobble a bit during rotation. Those tiny wobbles will not be perfectly repeated in reverse and so the coloured blobs become slightly smudged. The fold-back clips help keep the two glasses concentric, but it's a far-from-perfect arrangement. If you happen to find a better way to achieve the same result with readily available household materials, drop us a line or better yet, send us a video! In the meantime, happy unmixing.